Advanced Search

Let $𝒜={\left\{A_t\right\}}_{t\in G}$ and $ℬ={\left\{B_t\right\}}_{t\in G}$ be $C^{*}$-algebraic bundles over a finite group $G$. Let $C={⨁}_{t\in G}{A}_t$ and $D={⨁}_{t\in G}{B}_t$. Also, let $A=A_e$ and $B=B_e$, where $e$ is the unit element in $G$. We suppose that $C$ and $D$ are unital and $A$ and $B$ have the unit elements in $C$ and $D$, respectively. In this paper, we show that if there is an equivalence $𝒜-ℬ$-bundle over $G$ with some properties, then the unital inclusions of unital $C^{*}$-algebras $A\subset C$ and $B\subset D$ induced by $𝒜$ and $ℬ$ are strongly Morita equivalent. Also, we suppose that $𝒜$ and $ℬ$ are saturated and that $A^{\text{'}}\cap C=𝐂1$. We show that if $A\subset C$ and $B\subset D$...

Following Jansen and Waldmann, and Kajiwara and Watatani, we introduce notions of coactions of a finite-dimensional C*-Hopf algebra on a Hilbert C*-bimodule of finite type in the sense of Kajiwara and Watatani and define their crossed product. We investigate their basic properties and show that the strong Morita equivalence for coactions preserves the Rokhlin property for coactions of a finite-dimensional C*-Hopf algebra on unital C*-algebras.